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Fuzzy Logic 2 for Mathematica Provides Greater Flexibility for Exploring Fuzzy Systems

Published May 28, 2003

May 28, 2003–Fuzzy Logic 2 from Wolfram Research is an impressive update to this Mathematica application package that has been lauded by users as “the best fuzzy logic software currently available on the market.” Version 2 includes a large number of new functions that enhance the already robust set of utilities available with the package as well as other performance improvements resulting in part from the package’s ability to capitalize on advances in Mathematica 4 and subsequent versions.

Fuzzy Logic provides a flexible environment for creating, modifying, and visualizing fuzzy sets and fuzzy logic-based systems. Built-in functions help users through every stage of the design process to define inputs and outputs, create fuzzy set membership functions, manipulate and combine fuzzy sets and relations, apply inferencing functions to system models, and incorporate defuzzification routines. Ready-to-use graphics routines make it easy to visualize defuzzification strategies, fuzzy sets, and fuzzy relations.

New functionality in Fuzzy Logic 2 includes:

  • Broader definition of universal space, using three numbers that specify the start and end of the universal space and the increment between elements

  • New membership functions for creating special types of fuzzy sets, including bell-shaped, sigmoidal, two-sided Gaussian, and digital

  • New fuzzy graph visualization tool

  • New functions for finding the smallest and largest of maximum defuzzification and the bisector of area defuzzification of a fuzzy set

  • Operators for finding the fuzzy cardinality, degree of subsethood, Hamming distance, and alpha levels of or between fuzzy sets or relations

  • Yu and Weber union and intersection operations

  • Introduction of alpha cuts for fuzzy relations

  • Fuzzy relation equations

  • Random fuzzy sets and fuzzy relations functions

  • Fuzzy inferencing functions for rule-based inference

  • Fuzzy arithmetic functions for fuzzy multiplication and division

  • Fuzzy C-means clustering function for finding cluster centers and their associated partition matrices and progressions

The ease with which fuzzy sets and relations can be entered and manipulated in Fuzzy Logic makes this product ideally suited for professionals, researchers, educators, and students with all levels of experience in fuzzy logic theory. Engineers can use the package to research, model, test, and visualize real systems from the most basic to the highly complex. Researchers can use the comprehensive set of fuzzy logic tools to investigate applications of fuzzy theory and new ideas in the field. Educators can use Fuzzy Logic, either alone or as a complement to a class text, to teach concepts, basic theory, and applications of fuzzy logic. Students can use the included examples to help solve a large variety of problems in step-by-step detail.

Applications of fuzzy logic have taken root and grown in a wide variety of fields ranging from control, signal and image processing, and communications and networking to diagnostic medicine and finance. Because Fuzzy Logic is written in the Mathematica language, its functionality can be easily extended and modified to meet the precise needs of all types of users. Additionally, Fuzzy Logic can be used in conjunction with other Mathematica application packages designed for specialized areas or with unrelated software via MathLink.

Fuzzy Logic 2 is designed for use with Mathematica 4 or later and is available for Windows 95/98/Me/NT/2000/XP, Mac OS, Mac OS X, Linux (PC, Alpha, PowerPC), Solaris, HP-UX, IRIX, AIX, HP Tru64 Unix, and compatible systems.

More information about Fuzzy Logic 2 is available.